Systematic error-correcting codes for rank modulation

The rank-modulation scheme has been recently proposed for efficiently storing data in nonvolatile memories. In this paper, we explore [n, k, d] systematic error-correcting codes for rank modulation. Such codes have length n, k informa-tion symbols, and minimum distance d. Systematic codes have the benefits of enabling efficient information retrieval in conjunction with memory-scrubbing schemes. We study systematic codes for rank modulation under Kendall’s τ-metric as well as under the ∞-metric. In Kendall’s τ-metric, we present [k + 2, k, 3] systematic codes for correcting a single error, which have optimal rates, unless systematic perfect codes exist. We also study the design of multierror-correcting codes, and provide a construction of [k + t + 1, k,2t + 1] systematic codes, for large-enough k. We use nonconstructive arguments to show that for rank mod-ulation, systematic codes achieve the same capacity as general error-correcting codes. Finally, in the ∞-metric, we construct two [n, k, d] systematic multierror-correcting codes, the first for the case of d = O(1) and the second for d = (n). In the latter case, the codes have the same asymptotic rate as the best codes currently known in this metric